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प्रश्न
Which of the following matrices are singular or non singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
उत्तर
Let A = `[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
∴ |A| = `|("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")|`
Applying R3 → R3 + R2, we get
|A| = `|("a", "b", "c"),("p", "q", "r"),(2"a", 2"b", 2"c")|`
Taking 2 common from R3, we get
|A| = `2|("a", "b", "c"),("p", "q", "r"),("a", "b", "c")|`
= 2(0) ...[∵ R1 and R3 are identical]
= 0
∴ A is a singular martix.
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